Two-step code generator for phase coded frequency modulated continuous wave (fmcw) multi input multi output (mimo) radar

ABSTRACT

A two-step optimization method for scheduling transmissions in an MIMO (multi-input multi-output) includes determining a first phase code for each transmission according to a first equation, placing each first phase code in a set of first phase codes, and determining a cost function of the set of first phase codes, determining a second phase code for each transmission according to a second equation, determining an updated cost function corresponding to replacing each of the first phase codes with a corresponding one of the second phase codes, and determining which set of phase codes has a smaller cost function.

TECHNICAL FIELD

The present disclosure relates generally to phase coded frequencymodulated continuous wave MIMO radar, and more specifically to atwo-step code generation for the same.

BACKGROUND

Multi-input Multi-output (MIMO) radar is a type of phased array radarand employs digital receivers and waveform generators distributed acrossthe aperture. MIMO radar signals propagate similar to multistatic radar.However, instead of distributing the radar elements throughout thesurveillance area, antennas are closely located to obtain better spatialresolution, doppler resolution, and dynamic range. MIMO radar may alsobe used to obtain low-probability-of-intercept radar properties. Toimprove MIMO radar systems, the systems are designed with orthogonalsignals to support simultaneous transmission from multiple antennas.

Existing methodologies to design orthogonal signal based systems apply arandom offset to a conventional linear frequency modulation (LFM) signalfor the frequency modulated continuous wave MIMO radar operation. Somephysical systems are incapable of supporting such a random offset, orare suboptimal while implementing such a system.

SUMMARY OF THE INVENTION

In one example, a multi-input multi-output (MIMO) radar system includesa plurality of antenna, each antenna including at least one transmitterand at least one receiver arranged in a collocated configuration, acontroller including a non-transitory memory storing instructions forcausing the controller to schedule transmissions from the plurality ofantenna via determining a first phase code for each transmissionaccording to a first equation, placing each first phase code in a set offirst phase codes, and determining a cost function of the set of firstphase codes and determining a second phase code for each transmissionaccording to a second equation, determining an updated cost functioncorresponding to replacing each of the first phase codes with acorresponding one of the second phase codes and determining which set ofphase codes has a smaller cost function.

In another example of the above described MIMO radar system, the firstphase code for each transmission is determined with consideration toonly phase codes already determined.

In another example of any of the above described MIMO radar systems, thecost function of the first set of phase codes is determined via equation1.

In another example of any of the above described MIMO radar systems, thesecond phase code for each transmission is determined with considerationto phase codes corresponding to all transmitters in the plurality ofantenna.

In another example of any of the above described MIMO radar systems, thesecond phase code for each transmission is determined via equation 2.

In another example of any of the above described MIMO radar systems,each phase code in the first set of phase codes is a Binary Phase ShiftKeying Modulation (BPSK) phase code.

In another example of any of the above described MIMO radar systems,each phase code in the second set of phase codes is a Binary PhaseModulation (BPM) phase code.

In one example, a two-step optimization method for schedulingtransmissions includes determining a first phase code for eachtransmission according to a first equation, placing each first phasecode in a set of first phase codes, and determining a cost function ofthe set of first phase codes, determining a second phase code for eachtransmission according to a second equation, determining an updated costfunction corresponding to replacing each of the first phase codes with acorresponding one of the second phase codes, and determining which setof phase codes has a smaller cost function.

In another example of the above two-step optimization method forscheduling transmissions, the first phase code for each transmission isdetermined with consideration to only phase codes already determined.

In another example of any of the above two-step optimization methods forscheduling transmissions, the cost function of the first set of phasecodes is determined via equation 1.

In another example of any of the above two-step optimization methods forscheduling transmissions, the second phase code for each transmission isdetermined with consideration to phase codes corresponding to alltransmitters in a plurality of antenna.

In another example of any of the above two-step optimization methods forscheduling transmissions, the second phase code for each transmission isdetermined via equation 2.

In one example, a method for optimizing a multi-input multi-output radartransmission includes initializing an array of phase codes using a firstphase code generation process, the array of phase codes including aphase code corresponding to each of multiple transmitting antenna,generating a cost function of the array of phase codes, determining asecond phase code for a first transmitting antenna in the multipletransmitting antennas and generating an updated cost function replacingthe first phase code corresponding to the first antenna with the secondphase code corresponding to the first antenna, comparing the updatedcost function to the cost function and replacing the cost function withthe updated cost function in response to the updated cost function beingsmaller than the cost function, and iterating the step of determiningthe second phase code for the first transmitting antenna in the multipletransmitting antennas and generating an updated cost function replacingthe first phase code corresponding to the first antenna with the secondphase code corresponding to the first antenna, comparing the updatedcost function to the cost function and replacing the cost function withthe updated cost function in response to the updated cost function beingsmaller than the cost function until the cost function has eitherconverged or reached a maximum.

In another example of the above method, the first cost function isgenerated using equation 1.

In another example of any of the above methods, each updated costfunction is generated using equation 2.

In another example of any of the above methods, initializing the arrayof phase codes using the first phase code generation process includesiteratively generating phase codes.

In another example of any of the above methods, each iterativelygenerated phase code is optimized for previously generated phase codesand is not optimized for prospectively generated phase codes.

In another example of any of the above methods, each phase code in thearray of phase codes is a Binary Phase Shift Keying Modulation (BPSK)phase code.

In another example of any of the above methods, each phase code in thearray of phase codes is a Binary Phase Modulation (BPM) phase code.

In another example of any of the above methods, the step of determiningthe second phase code for the first transmitting antenna in the multipletransmitting antennas and generating an updated cost function replacingthe first phase code corresponding to the first antenna with the secondphase code corresponding to the first antenna, comparing the updatedcost function to the cost function and replacing the cost function withthe updated cost function in response to the updated cost function beingsmaller than the cost function until the cost function has eitherconverged or reached a maximum includes is iterated once for each phasecode in the array of phase codes.

These and other features of the present invention can be best understoodfrom the following specification and drawings, the following of which isa brief description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an exemplary multi-input multi-output radar system.

FIG. 2 schematically illustrates a particle swarm optimization for themulti-input multi-output radar system of FIG. 1.

FIG. 3 schematically illustrates a two-step optimization of the particleswarm optimization of FIG. 2.

DETAILED DESCRIPTION

FIG. 1 schematically illustrates an exemplary collocated multi-inputmulti-output (MIMO) radar system 10. The exemplary system 10 includes aprimary system 20 including a transmitter and receiver simultaneouslyreceiving multiple transmissions 30, and sending out multipletransmissions 32 to and from remote antennas 40. MIMO radar systems,such as the exemplary system 10, are systems of multiple antennas 40.Each of the antennas includes collocated transmit and receivecomponents. Each transmitting antenna 40 radiates an arbitrary waveformindependently of the other transmitting antennas 40. Each receivingantenna 40 can receive the signals 30 from the transmitting antennas 40.Due to the different waveforms, the echo signals can be re-assigned to asingle transmitter 40. From an antenna field of N transmitters 40, whereN is the number of transmitting antennas 40, and a field of K receivers40, where K is the number of receiving antenna 40, mathematicallyresults in a virtual field of K·N elements with an enlarged size of avirtual aperture. While illustrated in the example system 10 as threeconcurrently transmitting antennas 40 and three concurrently receivingantennas 40, it is understood that the number of concurrenttransmissions and receipts can be substantially larger in a practicalimplementation and three of each are illustrated in the example system10 for clarity. The utilization of collocated antenna 40 improves thedegrees of freedom of the transmitting end and allows for more degreesof freedom, higher target parameter identifiability and a higher angularresolution.

In order to optimize transmissions between the antennas 40, Binary PhaseShift Keying Modulation (BPSK) or Binary Phase Modulation (BPM) isapplied to each transmitter via a controller 22 included within theprimary system 20, with the controller 22 including a non-transitorymemory storing instructions for causing the controller 22 to implementthe scheduling process described below.

Assuming a system 10 having P transmission channels, P phase codes arerequired in order to implement the corresponding optimization system.Directly running the phase code optimization can lead, in some systems,to exponential increases in computational difficulty. When it does,current systems can perform sub optimally, or not at all depending onthe hardware implementing the MIMO system 10.

In order to optimize the phase codes, the system 10 uses a stackcontaining the phase codes, with the stack being an N×1 vector for theeach transmission in the stack, where N is the total number of inputs inthe MIMO radar system 10. Once the first transmission is on the stack,the initial phase code design of the second transmission is placed onthe stack, and this is iterated until there are P codes on the stack.Thus, in the first step, the optimization system used in the system 10optimizes each phase code as it is put on the stack, rather thanoptimizing the entire stack each time a phase code is added to thestack, thereby avoiding the exponential computational complexity. Thestack generated by the first step is referred to as the first set ofphase codes.

As the design of each phase code only considers the mutual interferenceto the phase codes already included in the stack, the performance of thephase code decreases as the number of transmissions increases. In orderto reduce the degradation of performance, the second optimization stepoccurs after the full transmission stack has been generated, andconsiders all of the transmission codes in the stack. The second stepconstructs a second set of phase codes and compares the second set ofphase codes to the first set of phase codes to determine which set has asmaller cost function.

With continued reference to FIG. 1, FIG. 2 illustrates an exemplaryoptimization process 100 implemented in the exemplary system 10. Thetwo-step MIMO code optimization process 100 is described with regards toa Binary Phase Modulation based phase code. One of skill in the art canadopt the process 100 to function with BPSK modulation.

Initially a size N BPM code is generated, where N is the number oftransmitting antenna 40 in the system 10 in an initialization step 110.Once the initial BPM code is determined, the code is saved as a testarray (C_(test)), and the level of sidelobes (referred to as the arrayscost function) is determined in a generate C_(test) step 120. Theinitialization step is repeated until the full array is created,resulting in P transmission codes. The initialization step 110 and thegenerate C_(test) step 120 combined form the first step (step 1) of thetwo-step algorithm disclosed herein, with the remainder combining toform the second step (step 2) of the two step algorithm.

Once the initial codes have been determined the system 100 iterates thegeneration of C_(test) by changing one value of C_(test) each iterationto generate N new codes in a generate new codes step 130. Aftergeneration of each new code, the cost function of the new code iscalculated and compared to the cost function of the previous Nth code ina comparison step 140. If the cost function of the updated code is lessthan the cost function of the previously saved code, then the new BPMcode is saved to the C_(test) code and replaces the old Nth code in areplacement step 150. If, instead, the updated cost function is not lessthan the previous cost function of the Nth code, the new BPM code isdiscarded and the existing BPM code is maintained in a maintain codestep 155.

After each code is either replaced or maintained, the process 100determines if the phase code C_(test) has converged, or has reached amaximum cost function value in a check for optimization step 160. If thecode has not converged or reached the maximum cost function value, theoptimization process 100 returns to the generate new codes step 130, andchanges the next C_(test) value. If the phase code C_(test) hasconverged or reached the maximum cost function value, the code is outputas the optimized code in an output step 170.

With continued reference to the general optimization procedure describedabove, and illustrated in FIG. 1, one example implementation of anexemplary specific optimization process.

In the first step (step 1) the codes c₁, c₂, . . . , c_(Q) fortransmission 1, transmission 2, . . . , transmission Q (where Q is thetransmissions number) are generated. In order to generate the next codefor the stack, the algorithm searches the codes for c_(Q+1) using aparticle swarm algorithm. The code vector c_(test) is initialized withvalues at +1 and at −1. This size of the code vector is N by 1, where Nis the code length. Then, the searching process is run to minimize agiven cost function. Note that a low DC component and small sidelobe forthe waveform is desirable and the cost function is given by equation (1)below.

$\begin{matrix}{{f\left( c_{Q + 1} \right)} = {{\sum\limits_{q = 1}^{Q}{\max{{{DFT}\left( {c_{q}c_{Q + 1}w} \right)}}}} + {\sum\limits_{q = 1}^{Q}{a\left\lbrack {{{DFT}\left( {c_{q}c_{Q + 1}w} \right)}} \right\rbrack}_{center\_ bins}}}} & (1)\end{matrix}$

In equation (1), w is a Chebyshev window, a is an adjustable weightingcoefficient, DFT(g) is the discrete Fourier transform. At this stage,the code optimization only considers the previous transmissions, so theperformance of each of the codes decreases as Q increases.

To avoid the degradation, and make the performance of the channels morebalanced, the code is optimized in step 2 for R=2, 3, . . . P with anupdated cost function defined in equation (2).

$\begin{matrix}{{g\left( c_{R} \right)} = {{\sum\limits_{{q = 1},{q \neq R}}^{P}{\max{{{DFT}\left( {c_{q}c_{R}w} \right)}}}} + {\sum\limits_{{q = 1},{q \neq R}}^{P}{a\left\lbrack {{{DFT}\left( {c_{q}c_{R}w} \right)}} \right\rbrack}_{{center}_{-}{bins}}}}} & (2)\end{matrix}$

With continued reference to FIGS. 1 and 2, FIG. 3 illustrates the endcode design using the following steps. Initially c₁ is set as all-onevector in an initialize vector step 210. Once initialized, theoptimization process of FIG. 2 is applied use the cost function definedin equation 1 for Q=1, 2, . . . , P−1, and the codes are initializedrandomly in a first cost function generation step 220. Once all of thecodes are initialized, step 2 of the optimization process is operated.In step 2, the updated cost function is determined according to equation2 for R=2, 3, . . . , P in a second cost function generation step 230,where R is the index of the channel for code optimization. Once theupdated cost function has been determined by equation 2, the comparisonstep 140 (shown in FIG. 2) is performed, and the end result is saved, ornot saved according to steps 150, 155. Finally, the phase codes areoutput in an optimized form in the output step 240, 170.

It is further understood that any of the above described concepts can beused alone or in combination with any or all of the other abovedescribed concepts. Although an embodiment of this invention has beendisclosed, a worker of ordinary skill in this art would recognize thatcertain modifications would come within the scope of this invention. Forthat reason, the following claims should be studied to determine thetrue scope and content of this invention.

1. A multi-input multi-output (MIMO) radar system comprising: aplurality of antenna, each antenna including at least one transmitterand at least one receiver arranged in a collocated configuration; acontroller including a non-transitory memory storing instructions forcausing the controller to schedule transmissions from the plurality ofantenna via determining a first phase code for each transmissionaccording to a first equation, placing each first phase code in a set offirst phase codes, and determining a cost function of the set of firstphase codes and determining a second phase code for each transmissionaccording to a second equation, determining an updated cost functioncorresponding to replacing each of the first phase codes with acorresponding one of the second phase codes and determining which set ofphase codes has a smaller cost function.
 2. The MIMO radar system ofclaim 1 wherein the first phase code for each transmission is determinedwith consideration to only phase codes already determined.
 3. The MIMOradar system of claim 2, wherein the cost function of the first set ofphase codes is determined via equation
 1. 4. The MIMO radar system ofclaim 1, wherein the second phase code for each transmission isdetermined with consideration to phase codes corresponding to alltransmitters in the plurality of antenna.
 5. The MIMO radar system ofclaim 4, wherein the second phase code for each transmission isdetermined via equation
 2. 6. The MIMO radar system of claim 1, whereineach phase code in the first set of phase codes is a Binary Phase ShiftKeying Modulation (BPSK) phase code.
 7. The MIMO radar system of claim1, wherein each phase code in the second set of phase codes is a BinaryPhase Modulation (BPM) phase code.
 8. A two-step optimization method forscheduling transmissions comprising: determining a first phase code foreach transmission according to a first equation; placing each firstphase code in a set of first phase codes, and determining a costfunction of the set of first phase codes; determining a second phasecode for each transmission according to a second equation; determiningan updated cost function corresponding to replacing each of the firstphase codes with a corresponding one of the second phase codes; anddetermining which set of phase codes has a smaller cost function.
 9. Thetwo-step optimization system of claim 8 wherein the first phase code foreach transmission is determined with consideration to only phase codesalready determined.
 10. The two-step optimization system of claim 9,wherein the cost function of the first set of phase codes is determinedvia equation
 1. 11. The two-step optimization system of claim 8, whereinthe second phase code for each transmission is determined withconsideration to phase codes corresponding to all transmitters in aplurality of antenna.
 12. The two-step optimization system of claim 11,wherein the second phase code for each transmission is determined viaequation
 2. 13. A method for optimizing a multi-input multi-output radartransmission comprising: initializing an array of phase codes using afirst phase code generation process, the array of phase codes includinga phase code corresponding to each of multiple transmitting antenna;generating a cost function of the array of phase codes; determining asecond phase code for a first transmitting antenna in the multipletransmitting antennas and generating an updated cost function replacingthe first phase code corresponding to the first antenna with the secondphase code corresponding to the first antenna, comparing the updatedcost function to the cost function and replacing the cost function withthe updated cost function in response to the updated cost function beingsmaller than the cost function; and iterating the step of determiningthe second phase code for the first transmitting antenna in the multipletransmitting antennas and generating an updated cost function replacingthe first phase code corresponding to the first antenna with the secondphase code corresponding to the first antenna, comparing the updatedcost function to the cost function and replacing the cost function withthe updated cost function in response to the updated cost function beingsmaller than the cost function until the cost function has eitherconverged or reached a maximum.
 14. The method of claim 13, wherein thefirst cost function is generated using equation
 1. 15. The method ofclaim 13, wherein each updated cost function is generated using equation2.
 16. The method of claim 13, wherein initializing the array of phasecodes using the first phase code generation process comprisesiteratively generating phase codes.
 17. The method of claim 16, whereineach iteratively generated phase code is optimized for previouslygenerated phase codes and is not optimized for prospectively generatedphase codes.
 18. The method of claim 13, wherein each phase code in thearray of phase codes is a Binary Phase Shift Keying Modulation (BPSK)phase code.
 19. The method of claim 13, wherein each phase code in thearray of phase codes is a Binary Phase Modulation (BPM) phase code. 20.The method of claim 13, wherein the step of determining the second phasecode for the first transmitting antenna in the multiple transmittingantennas and generating an updated cost function replacing the firstphase code corresponding to the first antenna with the second phase codecorresponding to the first antenna, comparing the updated cost functionto the cost function and replacing the cost function with the updatedcost function in response to the updated cost function being smallerthan the cost function until the cost function has either converged orreached a maximum comprises is iterated once for each phase code in thearray of phase codes.